14.2 Exercise 10 — Applied Probability

(See Exercise 21 from " Problems On Random Vectors and Joint Distributions", Exercise 31 from "Problems on Mathematical Expectation", and Exercise 29 from "Problems on Variance, Covariance, Linear Regression"). $f_{X Y} \left(t , u\right) = \frac{2}{13} \left(t + 2 u\right)$ , for $0 \leq t \leq 2$ , $0 \leq u \leq \min \left\{2 t , 3 - t\right\}$ .

The regression line of Y on X is $u = - 0 . 1359 t + 1 . 0839$ .

f_{X} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{12}{13} t^{2} + I_{\left(1 , 2\right]} \left(t\right) \frac{6}{13} \left(3 - t\right)

Pfeiffer, Applied Probability, 14.2 Problems on Conditional Expectation, Regression, exercise 10

AI Tutor